This could be a key statement "but I've been using AVAST for quite some time with no problems." If you have come to the end of your Update expiration (see about avast, Registration Key info), usually 14 months you will need to register again,
avast! 4 Home Registration.
Q: My licence key has expired, what to do?
http://www.avast.com/eng/faq-registration-license.html#idt_1442If it is still in date, your firewall (what is it ?) could be blocking avast.setup, ensure it is able to connect or no updates.